含时阻尼线性谐振子的量子不变量处理

在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论.     

用不变量方法求含时谐振子的波函数

利用辅助方程从含量谐振子的哈密量出发得到了两个不变量，利用这两个不变量求得了系统薛定谔方程的解。     

广义含时谐振子的压缩态和压缩数态

文中研究了广义含时谐振子系统的不变量和不变量的一般形式，并利用基本不变量构造了此含时系统的压缩态和压缩激态。     

再谈含时Schroedinger方程的求解方法

介绍了线性耦合含时量子系统厄米不变量算符的构造方法，并运用Ｌｅｗｉｓ－Ｒｉｅｓｅｎｆｅｌｄ量子不变量理论得到了一些含时薛定谔方程的精确解，同时也给出了系统时间演化算符的构造方法。     

受到与速度平方成正比的力的谐振子的普遍解

将Ermakov系统加以推广，得出受到与速度平方成正比的力的变频率谐振子的不变量，求出其普遍解．     

含时谐振子系统的时间演化及压缩态

研究了有压缩和驱动项的含时谐振子系统的时间演化.通过适当选取厄密不变量，得到含时谐振子系统的量子态时间演化的封闭解及该系统的时间演化算符，给出产生压缩态的条件，得出驱动项不影响系统压缩态的结论. 关键词：     

精确的量子化条件和不变量

提出并证明了一维量子系统和三维球对称量子系统的一个精确的量子化条件.在此精确量子化条件中, 除了通常的Nπ项外, 还有一积分项, 称为修正项. 发现该修正项正是在超对称量子力学中所谓的有形状不变势的量子系统的一个不变量，它不依赖于波函数的节点数.对这些系统, 可用基态能级和波函数确定此不变量的值, 从而由精确的量子化条件容易算出全部束缚态的能级. 计算得到能级的正确性又反过来验证了在有形状不变势的量子系统中此修正项确实是不变量.计算的有形状不变势的量子系统, 包括一维的有限方势阱、Morse势及其变形、R 关键词： 量子化条件 超对称量子力学 形状不变势 不变量     

双阱结构含时量子输运的微扰论及输运方程

利用Lewis-Riesenfeld不变量理论和与不变量有关的幺正变换方法研究了双阱结构含时量子 输运的微扰论.获得了双阱内含时薛定谔方程的精确解的完备集，在此基础上，把双阱与左 右热库的相互作用作为微挠，获得了双阱结构一阶近似下的输运方程，并在绝热近似下提供 了一种用于研究量子输运过程中几何相因子(Berry相因子)的方法. 关键词： 含时量子输运 输运方程 不变量 几何相因子     

受任意随时间变化外力作用的含时谐振子的压缩态

利用基本不变量构造了受任意随时间变化外力作用的质量随时间变化的谐振子的压缩态，并利用基本不变量得到了此含量系统不变量的一般形式。     

含时耦合谐振子系统的时间演化与双模压缩态

运用Lewis Riesenfeld不变量理论,通过适当地选取厄米不变量,得到了含驱动项和双模耦合项的含时耦合谐振子系统薛定谔方程的封闭解,给出了系统的演化算符及其产生双模光场的压缩态的条件,并得出系统压缩态的量子涨落与驱动项无关但与系统所处的初态有关的结论. 关键词： 含时耦合谐振子系统 Lewis Riesenfeld不变量理论 双模压缩态     

Third and fourth order invariants for one-dimensional time-dependent classical systems

The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t ^−4/3 q ^1/2. Alexander von Humboldt-Stiftung Fellow, on leave from the Department of Physics, Ramjas College (University of Delhi), Delhi 110 007, India.     

One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach

Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x ^2j 〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.     

On the dynamics created by a time-dependent Aharonov-Bohm flux

We study the dynamics of classical and quantum particles moving in a punctured plane under the influence of a homogeneous magnetic field and driven by a time-dependent singular flux tube through the hole.     

含时谐振子的动力学演化

利用含时量子变换理论,由量子变换理论中的变换矩阵,方便地给出了含时谐振子的演化算符,从而求得了含时谐振子的精确解. 关键词： 含时谐振子 含时量子变换 动力学演化     

On computing joint invariants of vector fields

A constructive version of the Frobenius integrability theorem–that can be programmed effectively–is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko et al. (2009).     

含时量子体系的对称性与守恒量

讨论了与时间相关(含时)量子体系的对称性,给出了含时力学量为守恒量的判据.     

Path integral analysis of harmonic oscillators with time-dependent mass

Two cases of forced harmonic oscillators with time dependent mass for which exact propagators can be evaluated are presented. From the exact propagators, normalized solutions of the corresponding Schrödinger equations are arrived at. Time-dependent invariants are also found.     

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

For a large class of time-dependent non-Hermitian Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzed further and shown to be quasi-exactly solvable. Technically we constructed the Lewis–Riesenfeld invariants making use of the metric picture, which is an equivalent alternative to the Schrödinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.     

The logic of quantum mechanics derived from classical general relativity

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.